Green water is the result of a protist bloom normally caused by excessive nutrients in the tank. Green water is not always an evil. In moderation, many fish actually seem to benefit from it according to Dr. Innes. Green water often occurs naturally in nature anyway. Think of some of the ponds you've seen.
The problem begins if the green water gets to the stage where it starts to get "soupy" or thick. At this point the protists can suddenly use up all the nutrients in the tank. When this happens, it triggers a massive die-off and decomposition of the organisms, taking much of the oxygen with it. The warning sign is when the green water turns yellow. If this occurs, minutes count and a massive water change becomes necessary. From what you've stated, you don't seem to be too near this stage yet.
Since this problem is caused by too many nutrients in the tank, you can do something about it. Usually a good, thorough tank cleaning, with a water change, can take care of the problem. Sunlight getting into the tank can contribute to the problem as well.
If you have a good group of healthy plants, they will out-compete the protists for nutrients. But for their health, you don't want to cut the light back too much. 8-9 hours a day should be good enough.
The link that Mr. Limpet gave you is a good one to follow if you want to kill the organisms involved, but it isn't dealing with the root cause of the problem. If that is not dealt with, the problem can return.